Yes. Generally, the law permits people to enter into contracts, including commercial leases, upon whatever terms the landlord and tenant agree. Therefore, if you sign a commercial lease for a store in a shopping center, for example, that is written to favor only the landlord, then, yes, you have effectively forfeited all rights not expressly granted to the you, the tenant, by the lease agreement.
The Arizona Residential Landlord and Tenant Act (the "ACT"), A.R.S. §§ 33-1301 to 33-1381, gives tenants many rights, but these statutes do not apply to "commercial" leases (i.e., rental of real property other than dwelling units). The Landlord and Tenant statutes that apply to commercial leases, A.R.S. §§ 33-301 to 33-381, give the tenant practically no rights. Presumably, the Arizona legislature felt that persons who rent dwelling units (i.e., apartments, homes, etc.) need more protection from landlords than persons who have the financial wherewithal to rent commercial real estate.
An example will best illustrate the drastic distinction between residential leases and commercial leases. The ACT requires that the landlord give a delinquent tenant a Five-Day Notice to Pay or Quit before initiating an eviction action. A.R.S. § 33-1368(B). Further, a residential tenant has an absolute right to pay the total amount owed (i.e., past due rent, late fees, court costs and attorneys' fees) and force the landlord to accept reinstatement of the lease. A.R.S. § 33-1368(B). A commercial landlord, however, when rent is in arrears for five days, may, at the landlord's option, either re-enter and take possession (i.e., lock the tenant out) or "without formal demand" commence an eviction action. A.R.S. § 33-361(A). Further, once the commercial landlord has terminated the lease, the tenant cannot (unless the landlord consents) reinstate the lease, even if s/he pays all amounts due (i.e., past due rent, late fees, court costs, attorneys' fees). As you can see, the rights afforded to residential tenants by the ACT greatly exceed the rights afforded commercial tenants by the statutes. Moreover, one of the statutes in the ACT prohibits landlords from attempting to take away any of the tenant’s rights that are granted by the ACT; meaning, a residential landlord cannot even put provisions in the residential rental agreement (even if signed by both parties) that take away any of the tenant’s rights under the ACT. The only way, then, for the commercial tenant to obtain more rights is to have these rights written into the lease agreement (i.e., the landlord cannot re-take possession for any type of default without five-days prior written notice).
Returning to the answer to the question: the solution to your problem is simple in theory, but sometimes difficult in practice. Read the "proposed" lease agreement very carefully and/or have your attorney review it. Note any changes that you would like made to the terms "offered" (remember, at this point, the terms contained in the lease agreement are merely the terms offered by the landlord). Ask the landlord to modify the lease to include the terms that you wish changed. The landlord may change all, some or none of the terms you desire. You will either ultimately come to an agreement with the landlord or not. If the vacancy factor for the type of property you are looking for is high, your chances of convincing the landlord to modify his/her offered terms is greater than when the occupancy factor is low. If the landlord simply will not budge, then look elsewhere for a location and terms that are acceptable. Again, your chances of finding alternate commercial space on terms you find acceptable are greater when the vacancy factor for the type of property you are looking for is high.
Some specific concerns that you will have as a new store owner in a shopping center are: (1) does your lease include a non-compete clause, so that the landlord cannot rent space in the same shopping center to a tenant with a similar business, (2) does the lease obligate you to remain for the entire term of the lease even if the anchor tenant terminates or vacates (an anchor tenant is normally the largest tenant in the shopping center and typically draws most customers to the shopping center; for example Home Depot or a grocery store), and (3) are you required to be open for business certain hours of the day and certain days? Naturally, there may also be many other concerns specific to the type of business you are running and/or the type of property that you are leasing.
Once you have signed the lease agreement, however, onerous or not, you are bound by the terms of the written lease agreement; there is no statutory recision period (i.e., you do not have a few days to "think about it" and cancel the deal without penalty). Only in the most exceptional circumstances will a court of law intervene and rule that a particular term is "unconscionable" (i.e., unenforceable) under the law.